The Power of Models: Modeling PowerConsumption for IoT devices

Borja Martinez, Marius Monton, Member, IEEE, and Joan Daniel Prades,

Abstract

Making more energy efficient technologies is still far from having those envisaged ubiquitous deployments (so called theInternet of Things, or the Industrial Internet), which will enable optimal industrial operation, and will contribute to improve thesocial welfare.

Today, it is possible to build a device which features this industrial wireless performance, and is able to in-node analyzethe acquired data. However, energy-dimensioning the device in order to meet the application requirements is not an easy task,especially when the reliability claimed for industrial applications faces up to the uncertainty introduced by energy harvesting.

Modeling and dimensioning the energy consumption of an application at pre-deployment or pre-production stages is of utmostimportance considering the critical requirements of IoT applications in terms of reduced cost, life-time, and available energy.

This paper presents a comprehensive model for the power consumption of wireless sensor nodes that accounts for all theenergy expenditures at system-level: communications, acquisition and processing. The model is only based on parameters thatcan be empirically quantified, once the platform (i.e., technology) and the application (i.e., operation conditions) are defined.This results in a new framework for the study and analysis the energy live-cycle within the applications, suitable to determine inadvance the specific weight of application parameters and to understand the tolerance margins and trade-offs in the system.

Index Terms

Low power models, Sensor system networks, networkable sensors, sensor system integration

B. Martınez is with Microelectronics and Electronic Systems Dpt., Universitat Autonoma de Barcelona, Spain and Worldsensing, Barcelona, Spain. (e-mail:borja.martinez@uab.cat)

M. Monton is with Microelectronics and Electronic Systems Dpt., Universitat Autonoma de Barcelona, Spain and Worldsensing, Barcelona, Spain.J.D. Prades is with MIND-IN2UB, Department of Electronics, Universitat de Barcelona, Spain.

IEEE SENSORS JOURNAL 1

The Power of Models: Modeling PowerConsumption for IoT devices

I. INTRODUCTION

ENERGETICALLY autonomous wireless sensors are thebackbone of the Internet of Things (IoT) [1]. To imple-

ment this concept each sensor node must be able to harvest,buffer and consume the energy available in the environment,in an efficient manner [2].

WSNAPPLICATION

SYSTEM (S.O.)

WIRELESS

CONNECTIONSENSING

ACQUISITION

(PHYSICAL PROCESS)

EDEV

WIRELESS

SENSOR DEVICE

RADIO

POWER

MANAGER

EBUF

ENERGY

BUFFER

ENERGY

HARVESTING

ESCV

Fig. 1. Generic energy model for IoT device.

Fig. 1 represents the three main blocks to optimize in thedesign of energy efficient nodes. First, the power managementunit collects energy from the ambient and converts it intousable electrical power, properly adapted to feed the followingblocks [3]. Second, the energy is buffered in a battery, a super-capacitor, or any other device capable of storing and releasingenergy [4]. Third, the energy is consumed in the device tocarry out the required sensing, processing and communicationtasks [5].

In this architecture, energy follows the energy flow model[3], described in Eq. (1); being E and P , energy and powerterms, respectively:

E(t=0)BUF +

t∫

τ=0

PSCV (τ)dτ ≥t∫

τ=0

PDEV (τ)dτ = EDEV (t) (1)

In this general model, the energy initially stored in the bufferEBUF and the additional energy scavenged from the mediumESCV =

∫PSCV dτ must be greater than the energy that the

device requires to operate EDEV =∫PDEV dτ throughout

the whole operation time t of the system. A natural constraintfollows from energy causality, which dictates that energycannot be used before it is available [6]; so Eq. (1) conditionmust hold strictly at any time.

This is analogous to the classic producer-consumer problemin computing (also known as the bounded-buffer problem)[7]. The problem involves two processes, the producer andthe consumer, sharing a common, fixed-size, buffer used as aqueue. The producer’s job is to generate pieces of data and

store them into the buffer. At the same time, the consumer isremoving data from the buffer. The problem is assuring thatthe producer won’t try to add data into a full buffer, and theconsumer won’t try to remove data from an empty buffer.

Thus, the energy flow in a wireless sensor device followsthis model closely. However, the consumer’s goal in energy-limited systems is not always to dispatch tasks from the queueas fast as possible. In fact, most of the time, the optimizationobjective will be more conservative in order to optimizepower consumption. Only in seldom occasions, the devicewill require an aggressive configuration, thus maximizing theprocessing performance [8]. This leads to alternative costfunctions that determine the energy policies of the device [9].

Recently, the topic of neutral design policies is thriving inthe Wireless Sensor Network (WSN) research community (see[10] and citations within). The concept of neutrality accountsfor the fact that the energy used, over the long term, should be,at most, equal to that harvested (ESCV (t)≥EDEV (t), t→∞).In other words, the energy stored in the first part of (E(t=0)

BUF inEq. (1)) is negligible after some time running. This is a generalcondition for the sensors to be energetically self-sufficient, thatis, unattended devices will ideally last for an unlimited periodof time [11].

In spite of its conceptual simplicity, the realization of suchfinely tuned powering schemes is extremely challenging andrequires the optimization of many design parameters that affectthe system performance in a complex way. In this context,system-level consumption models are a valuable tool to supportthe design of energy constrained devices.

In the past few years, a vast literature has emerged onenergy constrained WSN. Most of the developed work isfocused on network activity, i.e., how communications issuesaffect the device consumption. Other works are concernedwith the role of processors in the energy expenditure, oreven with specific details about the sensing process itself.However rarely this topic has been addressed from a systemlevel perspective. For this reason, the applicability of thesemodels into practical designs is still limited. Nevertheless, theyprovide useful insights into some of the design trade-offs.

Among the first group, mainly focused in the communi-cations side, it is worth noting the work presented in [12],which find optimal transmission policies. according to theexpected energy income. However this work is focused onthroughout maximization that is not always required in amore general case. More related to our approach is [13], thatdevelops a method for dimensioning the energy spent duringthe communication process. The basic idea is to estimate thepower consumption of wireless sensors based on the individualcontributions of each of the building blocks involved in thecommunication. Neither sampling techniques nor the cost of

2 IEEE SENSORS JOURNAL

the application itself are however considered.Regarding processing power, several measurement-based

methods can be found in the literature. Most of these models,like those presented in [14] or [15], use data obtained from aphysical target device and associate the processor instructionswith the corresponding energy cost. The total energy is theaggregate cost of all executed instructions that can be obtainedby running the application in an emulator. These works arefocused on the accurate energy profiling of the CPU andprocessor peripherals (FLASH, RAM, ADCs), but any ofthem take into consideration other components that have asignificant weight in energy consumption, mainly related tocommunications. The main advantage of these measurement-based methods is the high accuracy in the energy estimationobtained due to the use of actual values measured in the targetplatform.

Some recent approaches to model the use of scavengingtechniques in industrial wireless applications deal with thesampling energy, although the topic is still far from beingaddressed in deep. For instance, [16] assumes a dependencebetween the harvesting pattern and the applications needs,drawing a best effort policy: an application wakes up thesystem and transmits a packet when enough energy hasbeen harvested. The sampling contribution is estimated tocompute the total energy, but the work does not provide aclear modeling of the application energy requirements nor adetailed network energy consumption analysis. Besides, [15]evaluates the cost of capturing the sample from the processorside. The model is built based on the type of the executedassembly instructions, the number of accesses to the memoryas well as the analog-to-digital converter; but, the powerconsumption associated with external sensors and componentsis not computed. In general, the energy consumption by thesensor has been underestimated in the literature, and this partcan contribute strongly in the consumption of the device,particularly for active sensors (i.e., needing some excitation).

Finally, from a different perspective, [17] analyzes severalsystem-level design aspects of wireless embedded systems.This survey identifies the synergies between wireless sensornetworks and non-intrusive electrical-signal-based monitoringand fault diagnosis for industrial systems. The main scope isto provide a system overview of applications in a networkarchitecture. That paper also provides detailed analyses toaddress the real-world challenges in designing and deployingWSNs in practice, including wireless-link-quality dynamics,noise and interference on communication range and reliability.However, the impact of these system level issues on the energyconsumption is not clearly addressed.

As it may be inferred from this brief analysis, the modelsdeveloped so far only cover partial areas of the design space.However, the energy budget is a shared resource and, ingeneral, a systematic study of how energy is distributed inthe whole system has not been tackled in the literature.

In this work we aim to formalize a system-level energyconsumption model (the EDEV term in Eq. (1)) that can beeasily simulated and numerically evaluated. The developmentof the presented methodology is in part motivated by thelack of a rigorous and systematic approach to model the

PDEV

TPRC

TSYS

NS ·TS

ESYS

EPRC

TRCD

ENET TMSG

EACQ

P

t

Fig. 2. Characteristic time evolution of energy usage. The vertical dimensionrepresents the instantaneous power consumption of the device. Consequently,shaded areas depict the accumulated energy for each task. The dashed line inthe figure represents the average power of the device PDEV .

energy consumption for smart-sensor devices with the requiredsystem-wide view.

Our model combines ideas and strategies proposed in dif-ferent works with new evaluation approaches in order to endup with a whole system model. From a practical perspective,the model is only based on operational parameters that canbe easily quantified, either by design or by empirical esti-mation. We also demonstrate with two study cases that themodel can effectively assist on the design and simulation ofWSN systems, providing concrete answers to abstract problemformulations, as energy causality, neutrality or sustainability.

II. BOTTOM-UP MODELING OF ENERGY CONSUMPTION

Most of the industrial monitoring applications follow a com-mon operational pattern: data is acquired by some sensor of thesystem, processed in a controller unit and some informationis then sent through a wireless channel. This process repeatsover time, and the role of its duty cycle is fundamental in theenergy consumption: the smaller the duty cycle (which canbe achieved by shortening the active time or by lengtheningidle periods) the lower the average power. [DEL] the largerthe duty cycle the lower the average power.

Based on this assumption, the power required to operatea wireless sensor device can be broken down into threemain blocks: for data sensing or acquisition PACQ, for datahandling or processing PPRC , and data communication, ornetworking PNET . Additionally, a tiny fraction of the avail-able reservoir is intended for system management tasks, suchas running a real-time operating system (RTOS) or rising thesystem at periodic wake-ups. The needs of these managementtasks are gathered in this PSY S contribution. These elementstogether form Eq. (2): the general expression for the device’spower consumption PDEV .

PDEV = PNET + PACQ + PPRC + PSY S (2)

Fig. 2 shows a characteristic sequence of tasks for amonitoring application. The system wakes-up periodically toget a record with elapsed time of TRCD. For each cycle, threemain steps are executed: i) capture a set of NS samples with

XXXX et al.: THE POWER OF MODELS: MODELING POWER CONSUMPTION FOR IOT DEVICES 3

TS period; ii) run some process/analysis of the record 1 ofacquired samples, and iii) report gathered data, update serverinformation or trigger an alarm when an anomaly is detected,generating some radio traffic with TMSG intervals.

In Fig. 2, the vertical dimension represents the instantaneouspower consumption of the device. Consequently, shaded areasdepict the accumulated energy for each task. ENET standsfor the energy drained for communication tasks, EACQ foracquisition and EPRC for processing. Running in the back-ground, the operating system or scheduler executes differentsynchronization and coordination tasks, which may includenetwork management. This systematic activity is carried outwithin TSY S cycles, and demand an associated energy ESY S .For illustration purposes, the dashed line in the figure repre-sents the average power of the device PDEV .

The proposed model is based on an atomic breakdownof each building block of Eq. (2), interpreted within theFig. 2 framework. The instantaneous power consumption isintegrated over the duration of the corresponding task, and itscharacteristic temporal scale or period of repetition is thenaveraged out. In the next sections, we go into details on theanalysis of each building block.

A. Modeling Network Energy

1) Point to Point Communications: The simplest modelfor wireless communications consists of an interference-free,single-hop scenario. The Medium Access Control (MAC) layeris idealized; i.e., apart from transmission and reception, it doesnot introduce further energetic inefficiencies due to collisionsand idle times for floor acquisition. In this case, the powerconsumption can be estimated for each device independently.As any attempt at transmission is supposed to arrive to thedestination, the model does not need to cope with interferencescaused by other devices, congestion or any other collectiveissue.

Under these assumptions, the average power of the com-munications block can be expressed in terms of the energyrequired to send a radio message EMSG, and the time betweenconsecutive messages T (i)

MSG, as shown in Eq. (3). The indexi of the summation runs for all messages on the averagingperiod NMSG.

PNET =

NMSG∑

i=0

EMSG

T(i)MSG

(3)

The energy per message EMSG is a parameter that dependsmainly on the specific radio technology. Two main factorsgovern this contribution: radio power and transmission time.Radio power tends to be maximized to increase its range,although it is legally limited in each Industrial, Scientific andMedical (ISM) band. Instead, transmission time is a parameterdetermined mainly by the modulation: depending on how amessage is spread over time, it balances the complex trade-offbetween bit-rate (and thus consumption), range, reliability andimmunity to interferences. The study of this topic is of out of

1A record is defined as the process of waking up, taking a set of samplesand storing it into memory, ready to be processed.

0 1 2 3 4 5 6 7 8 9 10 0

20

40

60

80

100

I DEV[m

A]

t [s]

Fig. 3. Measured SIGFOX transmission energy consumption in terms of thecurrent drained IDEV . At T = 1.6s starts the transmission of the payload,which is repeated 3 times. [Legend Rev.]

the scope on this work, but it is a fundamental step of thesystem design flow.

Regarding the time between messages, T 0MSG can be con-

sidered a constant parameter for periodic reporting applica-tions. In this case, Eq. (3) reduces to a simpler expressiongiven by Eq. (4)

PNET =EMSG

T 0MSG

(4)

More generally, sensors nodes generate endogenous traffic,each one according to some distribution or stochastic processand the T 0

MSG becomes a random variable. The message pro-duction rate, characterized by a certain probability distribution,depends basically on the underlying physical process. Then,the time elapsed between consecutive messages in Eq. (3)should be characterized by an appropriate statistical estimatorE[ ]. Typically it is used the expected value of the distributiondefined as TMSG, leading to Eq. (5). This approximationshould be good enough for long-term averaging.

PNET ∼=EMSG

E [TMSG]=EMSG

TMSG

(5)

The energy cost associated with each transmission may inturn depend on multiple factors:• Retransmissions: some opportunistic approaches just re-

transmit the same message several times in order toincrease the probability of delivery success. In this case,the energy per message is multiplied by the number ofattempts NR.

PNET = NR · EMSG/TMSG (6)

Fig. 3 shows a snapshot of a radio transmission using aSIGFOX transceiver [18], an illustrative example of thisapproach.

• Radio power: most radio transceivers allow programmerssome control over transmission power, providing a trade-off between energy cost and distance range. Typically,the output level is selected from among a set of discretevalues NP , leading to a quantized energy scale [19].

PNET = E(NP )MSG/TMSG (7)

4 IEEE SENSORS JOURNAL

• Spreading factor: alternatively, some radio technologiescan operate with different spreading factors NSF [20].The spreading factor increases the communication range,but lowers the bit-rate of the transmission: as the trans-mission time increases, more energy is required (seeFig. 4). This behavior can be easily modeled by somesuitable function h( ), as detailed in the next section.

PNET = h(NSF , EMSG)/TMSG (8)

Despite the simplicity of this scenario, it covers a large num-ber of applications. In recent years, wireless low power com-munications are evolving towards a wide-area, low bit-rate,low-cost approaches, operating over distances long enoughto avoid multi-hop techniques. Companies like SIGFOX,Semtech with LoRa and Weightless are examples of use forthese technologies [18][20][21]. The wide range, combinedwith a low data-rate orientation, allows modeling the radioactivity of these devices within the point-to-point, unidirec-tional link and retransmission free assumptions.

0 1 2 3 4 5 6 7 80

10

20

30

40

50

60

I DEV[m

A]

t [s]

SF=7

(a) Transmission using Spreading Factor 7

0 1 2 3 4 5 6 7 80

10

20

30

40

50

60

I DEV[m

A]

t [s]

SF=12

(b) Transmission using Spreading Factor 12

Fig. 4. Measured Cycleo transmission energy consumption in terms of thecurrent drained IDEV , for two spreading factor levels: SF=7 and SF=12.[Legend Rev.]

2) Time Synchronized Networks: These technologies forma second main category of industrial low-power radios. In thiswork, we adopt the model derived in [22] for Time SlottedChannel Hopping networks (TSCH). For this reason, in thissection we only outline the basic features required for buildinga higher level system model.

TSCH networks show an ultra low power consumptionprofile due to the low power nature of IEEE802.15.4 compliantradios, and due to the fact that nodes are synchronized and

0 15 30 45 60 75 90 105 120 135 150 165 180 0

2

4

6

8

10

12

14

16

I NET[m

A]

t [ms]

(a) Slot-frame composed by 10 slots with 5 of them active.

(b) Example of two TSCH slot-frame configurations.

Fig. 5. Consumption charactersitics of a TSCH network. (a) Measured TSCHnetwork transmission energy consumption in terms of the current drainedINET . (b) Scheme of the time allocation in two slot-frame configurations.[Legend Rev.]

actions occur at specific moments in time, enabling nodes tooptimize the usage of their resources.

In a TSCH network, slots are grouped into slot-frameswhich repeat over time. Each type of slot has an energyconsumption profile related to the hardware and the activity itis performing (e.g. transmit, receive, sleep, etc.) as shown inFig. 5a.

The model used is based on profiling the energy consump-tion E(i)SLOT in each of those slots, counting the number ofslots of each type, and calculating the total energy of the slot-frame. The average power can be obtained by dividing thetotal energy ESF by the slot-frame period TSF , as indicatedby Eq. (9). Since slot-frames repeat cyclically, TSF representsthe characteristic temporal scale of the network.

PNET =ESFTSF

=1

TSF

NSLOTS∑

i=1

E(i)SLOT (9)

For the purpose of the presented methodology, the keyfeature is the impact of the network configuration on theenergy consumption of the application. In a TSCH net-work, the slot-frame period is determined by the number ofslots in the slot-frame and the time assigned to each slotTSF=NSLOT ·TSLOT . As TSLOT is a fixed network parame-ter, the slot-frame length NSLOT determines how often actionsrepeat, which usually depends on application requirements.

A node is only active in a few time-slots in the slot-frame,which are used to send or receive information. During the

XXXX et al.: THE POWER OF MODELS: MODELING POWER CONSUMPTION FOR IOT DEVICES 5

rest of non-active slots, the node remains switched off (sleep).Energy consumption can be reduced by increasing the lengthof the slot-frame, i.e., by inserting more sleep slots or bydisabling some active slots so that they become sleep slots.If the number of active slots remains constant and the slot-frame size increases, the ratio of sleep slots to total timeslots increases. Thus the average energy spent by the node islower. The same effect is obtained by changing active slots tosleep while maintaining the slot-frame size constant. However,the reduction of activity comes at the cost of less bandwidthand increased latency. Reliability is also compromised, as lessredundant links to neighbors are expected.

Fig. 5b shows an example of two TSCH slot-frame config-urations with a different number of slots N and M , assumingM>N . The first slot is used for network discovery by meansof Enhanced Beacons. Then K data slots for transmission andreception are common in both configurations. ConfigurationA has N−K sleep slots (unused), while Configuration Bhas M−K sleep slots, meaning that a node running in thisconfiguration will be idle for longer periods.

B. Modeling Data Acquisition Energy

Monitoring applications can be classified in two categories:regular sensing, i.e. with a fixed acquisition interval, andevent-driven sensing, i.e., characterized by some stochasticdistribution. In event-driven sensing, a random event triggersthe acquisition of a series of samples from the sensor. Thisevent can be internal to the sensor (e.g. a random trigger incompressed sensing [23]) or it can be a request for acquireddata coming from en external source (e.g. radio request fordata [24]).

Then, we can model the energy consumption of the acqui-sition component using Eq. (10).

EACQ =

{ESMP ·NS (Regular)ESMP ·N ′S · Pr(e) (Event)

(10)

In this expression, ESMP is the energy needed to acquireone sample (see Fig. 6), and NS is the number of samplestaken during one regular sensing interval. For event-drivenapplications, Pr(e) is the probability of an event occurringin one sensing interval, and N ′S is the number of samplestaken following the occurrence of an event.

Obviously, the model can be generalized in order to accountfor more than one regular sensing interval (with differentperiods and sampling requirements), as well as various eventtypes.

C. Modeling Local Data Processing Energy

To estimate the energy drained from the battery by anapplication task, we adopt a method proposed and validatedoriginally in [25]. Starting from a high level description ofthe algorithm (e.g. Matlab/Octave), the number of operationsto process the original sensed signal is recorded, accountingbasically for the number of arithmetic operations: additions,multiplications, divisions and comparisons, which are the mainactors in signal processing loops. Thus, depending on the

TSETT

(SNR )

TS

TON

(ADC)

TON

(SNR )

TON

(CPU)

TC

ESNS

EADC

TWUP

(CPU )

Sample1 Sample 2

P

t

ECPU

(a) Model consumption scheme

0 2 4 6 8 10 12 14 0

2

4

6

8

10

12

14

16

I DEV

[mA]

t [ms]

(b) Measured consumption

Fig. 6. Typical energy consumption breakdown for acquiring a couple ofsamples . In the model scheme (a), TC is the total capture time; TS thesampling period; T (SNS)

SETT the sensor setting time (time for the sensor tostabilize and start capturing data); T (CPU)

WP processor Wake-up time andstart acquisition; T (ADC)

ON time of the ADC Conversion; T (CPU)ON time the

processor reads sample from ADC and stores it in memory (b) Shows a realrecord of the current consumed to acquire two samples. [Legend Rev.]

selected hardware architecture, these counters are mappedinto the corresponding number of microcontroller (µC) clockcycles, and subsequently the latter is mapped into the corre-sponding energy expenditure.

This method offers accurate results as long as the CPUtasks rely mainly on arithmetic instructions (as digital signalprocessing algorithms do). However, it is no longer applicablewhen the µC is involved in non-arithmetic based tasks, likedealing with a protocol stack. In that case, alternative methodsbased on Instruction Set Simulators (ISS) can be used. [14].

III. EXTRACTION OF TECHNOLOGICAL PARAMETERS

For the sake of analytical tractability, we propose an inter-mediate fitting step to find a simple closed-form expressionof each of the individual contributions. As this step requiresexperimental measurements of the actual platform, it can beskipped in early stage developments (i.e., when the platformis not yet available), or if the required time and resources donot justify the additional benefit. Yet, this step is highly rec-ommended since fitting can significantly improve the accuracyof the model.

Before starting with measurements, it is worth noting afew considerations. First, consumption is directly measuredin terms of current, not power. Therefore, an appropriate con-version must be applied to use all the above formulation. Theactual power drained from the buffer is measured according to

6 IEEE SENSORS JOURNAL

PDEV =IDEV ·VBUF , where IDEV is defined as the currentmeasured at the output of the energy buffer, and VBUF thevoltage in its terminals (see Fig. 1) Moreover, the referencevalues in the datasheets of the components (chips, batteries,scavengers, etc.) are typically expressed in intensity units.However power on the component side is relative to the localvoltage. Then, for each individual component i connectedto the power domain j, the power is obtained according to:P(i,j)=I(i)V (j)

Obviously, all magnitudes must be compared in the samepower domain, i.e., voltage level. As measurements are easierat the buffer output, before power reaches the regulators orDC/DC converters or regulators,, it is recommended to operateon the buffer side. In fact, for any practical estimation, whatactually really matters is the load at the energy buffer.

The class of DC/DC converter and regulator determines howis the jump from one power domain to another. Switched-modeconverters basically preserve power (with some losses beingparametrized by their efficiency factor η). Then, to interpretcomponent currents as battery loads the proper conversion isgiven by:

Switched DC/DC :

POUT=ηPIN ⇒ I(i)DEV = I(i)

1

η

(V (j)

VBUF

)

Linear converters roughly preserve currents, provided thatthe minimum required voltage dropout δ is respected(VOUT>VIN + δ). Then, currents measured on the buffer sideand the actual currents of the device are approximately thesame:

LinearDC/DC :

IOUT ∼= IIN ⇒ I(i)DEV

∼= I(i)

While respecting these rules, models can be described incurrent units I instead of power P , and charge units Q insteadof energy E (i.e., normalized by the voltage). This methodavoids continuous conversions and facilitates experimentalmeasurements. When all the components share the same powerdomain, the conversion is almost direct.

A. Network Profiling

Profiling a valid model for the wireless communications re-quires first figuring out the functional dependence on selectedcontrol parameters. The procedure is in essence the same forall practical networks. First, one should identify a suitablecontrol parameter NX . Then, one can fit experimental data tothe analytical function or polynomial approximation H(NX)chosen to model h() in Eq. (8). The following examplesillustrate the procedure.

7 8 9 10 11 12 0

25

50

75

100

125

150

175

200

225

S.F.

QN

ET[m

C]

Experimental Data

Q= γ · 2NSF + δ

0.0 0.2 0.4 0.6 0.8 1.00

10

20

30

40

50

60

I DEV

[mA]

t [s]

SF=7

SF=8

SF=9

SF=10

SF=11

Fig. 7. Fitting LoRa spreading-factor to Eq. (11). [Legend Rev.]

1) Point to Point Communications: For the case of single-hop networks we are going to use LoRa by Semtech asan illustrative example. As mentioned before, LoRa usesdifferent spreading factors to tune the range and consumptionof the transmissions. Although it is a very specific technology,similar fitting strategies can be applied to other technologies.

To increase the range, LoRa uses configurable SpreadingFactor (SF), or the ratio between the chip rate and the symbolrate. This SF parameter can be configured from SF6 toSF12 (64 to 4096 chips/symbol since in LoRa modulation isperformed by representing each bit of payload information bymultiple chips of information), with an increase in the linkbudget of 14 dB in the highest SF. This ends with a reductionin bit-ratio, which affects the time needed to send a payload,and hence, the power consumed in each transmission.

Fig. 4 shows the current measured for transmissions withdifferent spreading factors. Basically, each step in the spread-ing factor scale doubles the time that radio spends in ac-tive state. This suggests that the charge per message canbe characterized by an exponential function in the formH(N)=O(h(N))=2N , leading to Eq. (11) as a tentative fittingfunction:

QNET ∼= QMSG · 2NSF + QB (11)

In the experiment shown in Fig. 7, the model is fittedwith a trial set of ∼100 samples for each modulation. Theerror bars represent the empirical dispersion obtained. Resultsdemonstrate that the postulated model is in full agreementwith measurements within the experimental error. Numericalvalues obtained are QMSG = 6.1µC and QB = 13.0µC withRMS Relative Error = 6.4%.

2) Time Synchronized Networks: To obtain a suitable fittingfunction, Eq. (9) points out that the average current is theratio between the charge of the slot-frame QSF and theperiod TSF . The charge can be roughly estimated based onthe number of active slots and the charge per active slotQSF∼=QMSG·NACT ; whilst the length of the slot-frame isdetermined by the number of slots and the duration of eachTSF=TSLOT ·NSLOTS [22]. Then, the average current can be

XXXX et al.: THE POWER OF MODELS: MODELING POWER CONSUMPTION FOR IOT DEVICES 7

approximated by Eq. (12), where IB represents the backgroundactivity of the µC to control the network (periodic wake-ups, synchronization messages, etc.), and it can be consideredconstant.

10 15 20 25 30 35 40 45 500.5

0.7

0.9

1.1

1.3

1.5

1.7

1.9

NSLOTS

I NET[m

A]

Experimental Data

I = γ NACT

TSL ·NSL+ δ

Fig. 8. Fitting parameters of TSCH networks to Eq. (12). [Legend Rev.]

INET ∼=QMSG ·NACTTSLOT ·NSLOTS

+ IB (12)

In Eq. (12), the duration of a timeslot TSLOT is a fixed net-work parameter. QMSG represents the average charge requiredper packet, and depends basically on the radio technology.This means that, once the number of active slots in the slot-frame NACT are scheduled, the number of slots NSLOTSin the frame becomes the control parameter for the net-work energy, giving the characteristic functional dependencyINET∝1/NSLOTS as observed in Fig. 8.

Fig. 8 shows the empirical fitting of Eq. (12) ob-tained for a GINA platform. This platform is basedon a 16 bit MSP430F2618 µC with a IEEE802.15.4-compliant AT86RF231 radio transceiver by Atmel and a ST-LIS344ALHTR 3-axis accelerometer. Details about the plat-form and numerical results can be found in [26].

12 13 14 15 16 17 18 19 200

50

100

150

200

250

300

350

Frequency

Q [µC]

Experimental Data

N(µ,σ2)

0 1 2 3 40

4

8

12

16

I ACQ

[mA]

t [ms]

Fig. 9. Fitting sampling charge of a sensor to a normal distribution N (µ, σ).[Legend Rev.]

B. Sampling Characterization

The current drained by the acquisition block can be rea-sonably approximated by Eq. (13), where the charge to getNS samples of a record is averaged over the time elapsedbetween consecutive records TRCD, i.e., the wake-up period.In this expression, QSNR can be interpreted as the averagecharge to get one sample, and comprise both the sensor andthe processor contributions (including the ADC conversion)represented in Fig. 6a, while IQ accounts for the stand-by orquiescent current of the sensor.

IACQ ∼=QSNR ·NSTRCD

+ IQ (13)

While in many situations the sampling period TS is de-termined by the underlying physical magnitude and filteringrequirements (e.g. anti-aliasing Low-Pass Filters), the timebetween consecutive records TRCD is scheduled from theapplication layer, thus providing a mechanism for balancingenergy consumption and sensing accuracy.

The value of QSNR can be obtained by fitting a setof experimental samples. To illustrate the procedure, Fig. 9summarizes an experiment performed to characterize a digitalmagnetometer sensor. The inset plot shows the current mea-sured during the acquisition process, with multiple samplessuperimposed to portray the variability between them. Thecharge of each individual sample is obtained by integrating themeasured current. The main plot in Fig. 9 shows the empiricaldistribution of a dataset of ∼1000 samples, fitted to a normaldistribution with µQ±σQ = 14.5±0.8µC. The average chargeper sample can thus be approximated to the mean value of thedistribution QSNR ≈ µQ.

C. Processing Profiling

128 256 512 10240.0

0.5

1.0

1.5

2.0

2.5

3.0

N

QFFT[m

C]

Experimental DataQ= βNlog(N)

0 0.1 0.2 0.3 0.40

2

4

6

8

N=128

N=256

N=512

N=1024

I PRC[m

A]

t [s]

Fig. 10. Fitting parameters of FFT computing to Eq. (14). The inset shows arecord of the current consumed to perform a FFT calculation with increasingnumber of samples. [Legend Rev.]

To extract a valid model for the processing contribution,it is important first to identify the parameters that rule thealgorithm behavior. For already known algorithms a naturalchoice is the (worst-case) time complexity T (n). On the other

8 IEEE SENSORS JOURNAL

hand, if the algorithm is custom designed or its complexityis unknown, the fitting function should be inferred from theexperimental data or simulator.

To illustrate this idea with an example we use theFast Fourier Transform (FFT) algorithm. The FFT has awell known T (N)=O(f(N))=N log(N) complexity. Ac-cordingly, the associated processing time should be propor-tional to this relation. Considering QOP to be an estimate ofthe average cost per arithmetic operation, Eq. (14) can fit theprocessing power consumption with reasonable accuracy, asshown in Fig. 10.

IPRC ∼=k QOP ·N log(N)

TRCD+ ISY S (14)

In Eq. (14), k is a constant factor that depends on thealgorithm’s implementation, in this case, it is related to thenumber of arithmetic operations per FFT point. In turn, ISY Sincludes all system related functionalities of the µC, suchas running the operating system itself, managing periodicinterrupts, etc.

D. Putting the Pieces Together

The last step in the modeling process consist of mergingall contributions into one single expression. Followed byexamples, Eq. (15) combines the contributions coming fromsections III-B, III-A and III-C, keeping technological andapplication parameters as independent variables.

IDEV =αNSTRCD

+β · T (NP )

TRCD+γ · H(NA)

TMSG+ δ (15)

Constants α, β, γ and δ depend only on the particular choiceof sensor, µC and radio technologies. Recalling the meaningof each individual contribution from the fitting process, α canbe interpreted as the charge per sample QS , β is related withthe cost per operation QOP associated with the specific µCand algorithm, while γ is an estimator of the average chargeper message QMSG. All constant contributions related withsystem activity have been gathered in the δ term. Arrangedin this way, Eq. (15) allows for a straightforward evaluationof alternative technologies by simply finding the characteristicvalues for this set of parameters.

In turn, TMSG, Ni or TRCD are application parametersthat can be tuned in order to meet the specifications, oncethe specific technology has been established. In Eq. (15), NSstands for the number of samples effectively acquired in eachsampling interval, NP parametrizes the amount of data to beprocessed, and NA represents any parameter related to radioactivity.

The benefits drawn from this methodology relay on reachingEq. (15) starting from the vague condition asserted in Eq. (2).Once this general expression is properly interpreted accordingto the specific platform (technological parameters) and appli-cation (operational parameters), the outcome naturally emergeswhen exploiting by simulation the analytical model built, i.e.,the particular instance derived from Eq. (15). Next sectionspresent two case-studies to demonstrate the applicability ofthe presented methodology.

0 5 10 15 20 25 300

10

20

30

40

50

60

70

80

Sen

sorCou

nt

NMSG [1/day]

Fig. 11. Traffic generated by ∼500 parking spot sensors. Data was collectedover 100 days.

IV. CASE STUDY I: PERIODIC REPORTING APPLICATIONS

A. Network Scenario

New radio transceivers are evolving towards long rangemodulation techniques while maintaining low energy con-sumption, thus being suitable for battery powered devices andbecoming true enablers of the IoT.

A notable example of this new technological paradigmis Weightless, an industry consortium originally founded byNEUL with more than 1.000 members [21]. Weightless fostersthe development of wide-area communication in white spacesat sub-GHz ISM band, covering ranges of up to 10km.This communication scheme is based on costly and powerfulbase-stations managing the whole network. The devices aresynchronized and can send packets only in their time-slot.The packets are acknowledged to reduce packet loss and givefeedback about transmission parameters (transmission power,channel, spread-factor, etc.).

Another example of wide-range wireless connectivity forM2M (Machine-to-Machine) is SIGFOX [18], which uses asimple radio technology known as Ultra Narrow Band (UNB),and operates in the license-free ISM frequency band of 868MHz. As a MAC protocol, it uses retransmission of eachpacket in order to avoid packet loss. This technology is notbidirectional yet (only up-link is available).

Cycleo (now Semtech) is another provider of low-power,wide-area equipment operating in the sub GHz ISM band [20].It is based on their proprietary approach called LoRa. Thisnetwork topology is based on a base-station listening in severalbands. Synchronized devices can send packets in its own time-slot and wait for the ACK of every packet. This ACK packetscan carry some feedback information and the notification ofan incoming downlink packet.

All these examples are practical realizations of the networkscenario studied in this case study.

B. Application Scenario

Smart-parking systems provide an excellent applicationexample for this case study, based on the previous networkapproaches. On-street parking sensors are small devices used

XXXX et al.: THE POWER OF MODELS: MODELING POWER CONSUMPTION FOR IOT DEVICES 9

to monitor the availability of parking spots. Each deviceperiodically wakes-up to check the state of the spot. Whena car parks above, its presence is detected and the sensorreports the event to a gateway. The bandwidth required forthis application is particularly low, and thus perfectly suitedfor long-range radio technologies. The typical interval timebetween radio messages oscillates from some minutes toseveral hours, and the information required per message isvery small, as the state can be codified with just 1 bit.

Data generated from one single parking sensor is unpre-dictable; however, when data coming from a set of similar sen-sors is aggregated, a typical Poisson-like distribution emerges.Fig. 11 shows an example of the empirical distribution foundin a parking application. The histogram was obtained fromthe events gathered by a set of sensors belonging locatedin the same area and operating over several days. The solidline represents the fitted Poisson distribution. In this case, theexpected value of the number of messages per day is given bythe Poisson mean E[NMSG]=λMSG, and it is used to estimatethe average elapsed time between messages TMSG=1/λMSG,required for Eq. (3).

C. Model Description

In this kind of application, a record of NS samples isacquired with a fixed interval time TRCD. In addition, infor-mation is reported to the data collector center, with an updateperiod characterized by TMSG. In this simple approach, thereported information is aggregated in a unique message. Wealso assume that this message is retransmitted a certain numberof times NR to increase the probability of success, thus follow-ing the SIGFOX approach, as an alternative to implementingan acknowledgment scheme over a downlink of a LoRa-likeapproaches. In this case, the functional dependence associatedwith network retransmission is trivial H(NR)=NR, and γ iseasily interpreted as the charge per message QMSG.

Usually, the number of samples acquired NS equals thenumber of samples processed NP , thus we redefine this num-ber as N from this point on. This means that the N parameteraffects simultaneously consumption terms of both sensing andprocessing tasks. However, as this particular case is just areporting application, the cost associated with processing isvery low, and the associated term can be omitted. Then,Eq. (16) combines Eq. (6) and Eq. (13) in a basic instanceof Eq. (15).

IDEV =αN

TRCD+

γNRTMSG

+ δ (16)

D. Simulation Results

Fig. 12 presents a simulation obtained by applying Eq. (16)to different sampling TRCD and reporting period TMSG

configurations. The bars present the contribution to the en-ergy consumption of the network and sampling components,according to the time elapsed between consecutive messagesand the sampling rate. The floor level is associated with systemmanagement (e.g. periodic interrupts of the operating system).Although it is constant, this contribution carries important

4.03.5

3.02.5

2.01.5

1.00.5

10

20

30

40

50

60

0.0

0.1

0.2

0.3

0.4

0.5

0.6

TRCD [s]TMSG [min]

I DEV[m

A]

ProcessingSensorRadioSystem

Fig. 12. Simulated consumption for a simple periodic-reporting applicationas function of TMSG and TRCD . [Legend Rev.]

weight in this application. The main reason for this is the lowradio activity of the application that makes radio contributiona non-dominant term (in contrast with the usual assumptionin the literature). Processing cost is also represented, despitebeing negligible for this particular applications.

Asymptotic behavior of Eq. (16) is evident in both axesof Fig. 12. By maintaining a fixed recording interval time,the overall energy consumption is reduced when radio activityis lower. However, the amount of energy that can be savedis limited by the asymptotic decreasing. At a certain point,increasing the elapsed time between messages does not signif-icantly reduce the consumption. Analogously, as the recordinginterval increases, the energy savings decrease.

This graphical representation is useful as a tool for de-termining which control parameters are accountable for thehighest energy savings, as well as figuring out the achievablegains and limits for optimization.

E. Validation

In order to validate the previous estimations of the powerconsumption, a set of measurements have been performed on areal hardware system. The employed platform was composedof a Cortex-M4 32 bit µC, the Telecom Designs TD1202 long-range radio module, and the integrated Honeywell HMC5883digital compass. The RTOS wokes-up periodically with asystick period of 1 ms.

The application was configured with different samplingintervals TRCD, and different reporting periodicity TMSG.Fig. 13 compares the experimental results (dots) with thosepredicted by the model in Eq. (16) (vertical bars). Error barsaccount for the statistical deviation in the fitting process.Clearly, the prediction of the model agree with the experi-mental determinations of the system consumption, within theexperimental uncertainty.

This example has shown the work-flow with a few concretesteps to have a valid consumption model of a given platform.

10 IEEE SENSORS JOURNAL

It also showed the right outcome of the model in form of theconsumption foreseen for a specific application.

1 0.5 0.250.0

0.2

0.4

0.6

0.8

1.0

I DEV[m

A]

TRCD [s]

TMSG = 60 [min]TMSG = 30 [min]TMSG = 15 [min]

Fig. 13. Model validation of a simple periodic-reporting application [LegendRev.]

V. CASE STUDY II: TIME SLOTTED CHANNEL HOPPINGNETWORKS

A. Network Scenario

Industrial Wireless Mesh networks are being consolidatedby standardization efforts under the Time Slotted ChannelHopping (TSCH) scheme. This technique has been adoptedby major industrial low-power wireless standards such asWirelessHART [27], ISA100.11a [28], and, more recently,as a part of the IEEE802.15.4e standard [29]. As of today,several commercial low-power wireless networking providersare offering almost 100% reliable MAC layers, e.g [30], thatprovide radio duty cycles well below 1%, thereby reducingpower consumption, and increasing network lifetime. This isfacilitating the introduction of new monitoring and actuatingdevices that aim to improve the security, process automation,efficiency and productivity of the industries; Furthermore itdevises a clear roadmap for the Industrial Internet paradigm.Nowadays industrial wireless communications is considered amature technology.

B. Application Scenario

Notable examples of industrial wireless systems are vi-brational analysis of rotary machines [26], structural healthmonitoring through harmonic analysis, e.g. accelerometers formonitoring power-line towers [31], and vibrating wire straingauges [32] for measuring infrastructures. All these examplesinvolve some kind of frequency analysis that can be performedby means of the FFT algorithm, which has been chosen forillustrative purposes in this second case-study.

C. Model Description

This second example models an application that requiresarithmetic computing for the FFT. On top, the processor man-ages communications through a TSCH network. Therefore,Eq. (17) combines the contribution of Eq. (13), Eq. (12) andEq. (14)

IDEV =αN

TRCD+βNlog(N)

TRCD+

γNACTTSLOTNSLOTS

+ δ (17)

The main parameter involved in network consumption nowis NSLOTS , which is related to the number of active and sleepslots. Assuming a fix number of active slots, by incrementingNSLOTS we are introducing sleep slots to the schedule; there-fore reducing the average consumption, although sacrificingbandwidth and latency.

Following Fig. 2, the processor periodically wakes up,takes NS samples, and analyzes them. Again, the numberof points computed by the FFT NP , and the number ofsamples read by the ADC NS are the same. So, this parametersimultaneously affects both contributions, and it is denotedsimply by N . Fixed N is the duty-cycled behavior of theapplication and it makes the time between records TRCDthe fundamental parameter for controlling the average power.Specifically, as the time between records increases, less poweris consumed. Therefore, the time interval between consecutiverecords determines the time scale for power averaging.

D. Simulation Results

20

30

40

5010

20

30

40

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

2565

12

10242

565

12

10242

565

12

10242

565

12

1024

I AVG[m

A]

ProcessingSensingNetworkSystem

TRCD [s] NSLOTS

Fig. 14. Simulated consumption for an application using a TSCH network ,as function of NSLOTS and TRCD , for different number of samples in theFFT calculation NFFT . [Legend Rev.]

Fig. 14 presents the consumption values obtained by ap-plying Eq. (17) to different network NSLOTS and recordingperiod configurations TRCD, considering NFFT = 256, 512and 1024 samples per record. The bars present the contributionto the energy consumption of the network, sampling andprocessing components; according to the number of slots perslot-frame and the recording interval.

Again, asymptotic behavior appears in both axes of Fig. 14.While maintaining a fixed interval time, the overall energyconsumption is reduced by increasing the number of slots ina slot-frame. Still, the asymptotic behavior sets a limit to thepower savings: at a certain point, increasing the number ofslots in the network does not significantly reduce the energyconsumed.

XXXX et al.: THE POWER OF MODELS: MODELING POWER CONSUMPTION FOR IOT DEVICES 11

E. Validation

Experiments were carried out using a GINA platform [33],and running the OpenWSN protocol stack [34]. The GINAplatform comprises several inertial sensors for angular rate andlinear acceleration along with a general purpose microproces-sor. Specifically, constants α, β, γ and δ of Eq. (17) havebeen characterized for the Texas Instruments MSP430f261816-bit µC, Atmel AT86RF231 IEEE802.15.4 radio, and theST-LIS344ALHTR 3-axis accelerometer sensor.

Fig. 15 compares the experimental results (dots and exper-imental dispersion bars) with those predicted (vertical bars)by Eq. (17) for different application configurations: differentnumber of slots in a slot-frame NSLOTS , different recordingintervals TRCD, and different number of samples collected andprocessed NFFT . Again, the here-presented model quantita-tively predicts the experimental trends.

This example serves to further demonstrate the applicabilityof the model. A device operating in a real scenario hasalways a degree of uncertainty associated with environmentalconditions. Variations in the Packet Delivery Ratio (PDR) arejust a representative example, but also other issues as temporallink interruptions, unexpected system restarts, etc. Under thesecircumstances, further refinements for improving the accuracyof estimates may not be necessary. Instead, the strength of themodel lies in its capability to support better-informed decisionsand avoid risks in the early stages of development.

VI. CONCLUSIONS

The present paper defines a general methodology to modelenergy consumption of wireless network devices as a system.The model takes into account all the components that play afundamental role in a realistic industrial application: standardnetworking, mainly standard networking sensing and pro-cessing technologies. Our approach bridges the gap betweentheoretical analysis and practical applicability by proposinga straight forward method to estimate a few key parametersrelated to the technology used and the operation conditions ofa specific application.

The utility of the approach is illustrated with two casestudies. The agreement between experiments and predictionsdemonstrate that the model is valid and applicable to realapplications and platforms. It also shows that measuring a setof application-specific parameters is enough the make accurateestimations of the power consumption.

With this model, application engineers can foresee theimpact of different application parameters on power con-sumption, even without a complete implementation of theapplication. Hence, this framework can help engineers tostudy the viability of a new application in terms of powerconsumption, energy harvesting needs, battery requirements,etc.

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